TY  - JOUR
AU  - Salama, Fouad Mohammad
AU  - Hamid, Nur Nadiah Abd
AU  - Ali, Norhashidah Hj. Mohd
AU  - Ali, Umair
PY  - 2022
TI  - An efficient modified hybrid explicit group iterative method for the time-fractional diffusion equation in two space dimensions
JO  - AIMS Mathematics
SP  - 2370
EP  - 2392
VL  - 7
IS  - 2
AB  - In this paper, a new modified hybrid explicit group (MHEG) iterative method is presented for the efficient and accurate numerical solution of a time-fractional diffusion equation in two space dimensions. The time fractional derivative is defined in the Caputo sense. In the proposed method, a Laplace transformation is used in the temporal domain, and, for the spatial discretization, a new finite difference scheme based on grouping strategy is considered. The unique solvability, unconditional stability and convergence are thoroughly proved by the matrix analysis method. Comparison of numerical results with analytical and other approximate solutions indicates the viability and efficiency of the proposed algorithm.
UR  - https://doi.org/10.3934/math.2022134
DO  - 10.3934/math.2022134